capm vs market model

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SIES College of Management

Studies, NerulSub: Security Analysis and Portfolio Management

Topic: CAPM and Market Model

Prepared By:

Names Roll No.

Venkatesh Chary 6

Priya Mani 49

Divya Kudva 75

Naresh Naiker 79

Richa Varu 97

Siddarth Seth 99

Mohuddin Memon 116



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INTRODUCTION

The objective of every rational investor is to maximize his returns and minimize the risk.

Diversification is the method adopted for reducing risk. It essentially results in the constructionof portfolios. The proper goal of portfolio construction would be to generate a portfolio that

provides the highest return and the lowest risk. Such a portfolio would be known as the optimal

portfolio. The process of finding the optimal portfolio is described as portfolio selection.

The conceptual framework and analytical tools for determining the optimal portfolio in

disciplined and objective manner have been provided by Harry Markowitz in his pioneering

work on portfolio analysis. His method of portfolio selection has come to be known as the

Markowitz model.

FEASIBLE SET OF PORTFOLIOS

With a limited number of securities an investor can create a very large number of portfolios by

combining these securities in different proportions. These constitute the feasible set of portfolios

in which the investor can possibly invest. This is also known as the portfolio opportunity set.

Each portfolio in the opportunity set is characterized by an expected return and a measure of risk,

viz., variance or standard deviation of returns. Not every portfolio in the portfolio opportunity set

is of interest to an investor. In the opportunity set some portfolio in the opportunity set some

portfolios will obviously be dominated by others. A portfolio will dominate another if it has

either a lower standard deviation and the same expected return as other, or a higher expected

return and the same deviation as other. Portfolios are dominated by other portfolios are known as

inefficient portfolios.

EFFICIENT SET OF PORTFOLIOS

To understand the concept of efficient portfolios, let us consider various combinations of

securities and designate them as portfolios 1 to n. The expected returns of these portfolios may

be worked out The risk of these portfolios may be estimated by measuring the standard deviation



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of portfolio returns. The table below shows illustrative figures for the expected returns and

standard deviations of some portfolios.

PORTFOLIO EXPECTED

STD.

DEV.

NO. RETURNS (%) (RISK)

1 5.6 4.5

2 7.8 5.8

3 9.2 7.6

4 10.5 8.1

5 11.7 8.1

6 12.4 9.3

7 13.5 9.5

8 13.5 11.3

9 15.7 12.7

10 16.8 12.9

If we compare Portfolio no.4 and 5, for the same standard deviation of 8.1 Portfolio no. 5 gives a

higher expected return of 11.7, making it more efficient than portfolio no. 4.Again if we compare

Portfolio no. 7 and 8 for the same expected return the standard deviation is lower for Portfolio

no.7 making it more efficient than Portfolio no. 8

Thus the selection of portfolios by the investors will be guided by two criteria:

Given two portfolios with same expected return, the investor would prefer the one with

lower risk

Given two portfolio with same risk the investor would prefer the one with higher

expected returns



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This criteria are based on the assumption that investors are rational and also risk averse. As they

are rational they would prefer more return to less return .As they are risk averse, they would

prefer less risk to more risk.

The concept of efficient sets can be illustrated with the help of a graph. The expected return and

standard deviation of portfolios can be depicted on X Y graph, measuring the expected return on

the Y axis and the standard deviation on the X axis. Figure below depicts such a graph.

As each possible portfolio in the opportunity set or feasible set of portfolios has an expected

return and standard deviation associated with it , each portfolio would be represented by a

single point in the risk return space enclosed within the two axes of the graph .The shaded

area in the graph represents the set of all possible portfolios that can be constructed from a

given set of securities. This opportunity set of portfolios take a concave shape because it

consists of portfolios containing securities that are less than perfectly co related with each

other .

Consider portfolio F and E .Both the portfolios have the same expected returns but portfolio

E has less risk .hence, E would be preferred to F. Now consider C and E both have the same

risk ,but E offers more return for the same risk hence E would be preferred to C. Thus for

any point in risk return space, an investor would like to move as far as possible in the



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direction of increasing returns and also as far as possible in the direction of decreasing risk.

Effectively, he would be moving towards the left in search of decreasing risk and upwards in

search of increasing returns.

Now let us consider portfolios C and A .Portfolio C would be preferred to A as it offers less

risk for the same level of return. In the opportunity set of portfolios represented in the

diagram, C has the lowest risk compared to all other portfolios .Here C in the diagram

represents the global minimum variance portfolio.

Comparing portfolios A and B we find that portfolio B is preferable to A because it offers

higher returns for the same level of risk. In the diagram Point B represents the portfolio with

highest expected returns among all the portfolios in the feasible set

Thus we find that portfolios lying in the north west boundaries of the shaded areas are more

efficient than all the portfolios in the interior of the shaded areas.

This boundary of shaded area is called the efficient frontier because it contains all the

efficient portfolios in the opportunity set. The set of portfolios lying in between the global

minimum variance portfolio and the maximum return portfolio on the efficient frontier

represents the efficient set of portfolios.



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The efficient frontier is a concave curve in the risk return space that extends from the minimum

variance portfolio to the maximum return portfolio.

SELECTION OF OPTIMAL PORTFOLIO

The portfolio selection problem is really the process of delineating the efficient portfolios

and selecting the best portfolio from the set.

Rational investors will obviously prefer to invest in the efficient portfolios. The particular

portfolio that an individual investor will select from the efficient frontier will depend on that

investor’s degree of aversion to risk.

A highly risk averse investor will hold portfolio on the lower left hand segment of the

efficient frontiers, while an investor who is not too risk averse will hold one on the upper

portion of efficient frontier .

The selection of optimal portfolio thus depends on the investors risk aversion, or conversely

on his risk tolerance .This can be graphically represented through a series of risk return utility

curves or indifference curves. The indifference curves of an investor are shown in the figure.

Each curve represents different combinations of risk and return all of which are equally

satisfactory to the concerned investor. The investor is indifferent between the successive

points in the curve. Each successive curve moving upwards to the left represents a higher

level of satisfaction or utility. The investor’s goal would be to maximize his utility by

moving upto the higher utility curve. The optimal portfolio for an investor would be the one

at the point of tangency between the efficient frontier and his risk return utility or

indifference curve.



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The point O’ represents the optimal portfolio .Markowitz used the technique of quadratic

programming to identify the efficient portfolios. Using the expected returns and risk of each

security under consideration and the co variance estimates for each one of securities, he

calculated risk and return for all possible portfolios. Then, for any specific value of expected

portfolio return, he determined the least risk portfolio using quadratic programming. With

another value of expected portfolio return, a similar procedure again gives the minimum risk

portfolio. The process is repeated with different values of expected return, the resulting

minimum risk portfolios constitute the set of efficient portfolios.



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Limitations of Markowitz Model:

One of the main problems with the Markowitz model is the large number of input data required

for calculations. An investor must obtain estimates of return & variance of returns for all

securities as also co variances of returns for each pair of securities included in the portfolio. If

there are ‘N’ securities in the portfolio, an investor would need ‘N’ return estimates, ‘N’ variance

estimates & ‘N (N-1)/2 co variance estimates, resulting in a total of ‘2N + [N (N-1)/2] estimates.

For example, analyzing a set of 200 securities would require 200 return estimates, 200 variance

estimates & 19,900 co variance estimates, adding up to a total of 20,300 estimates.

The second difficulty with the Markowitz model is the complexity of computations required. The

computations required are numerous & complex in nature. With a given set of securities infinite

number of portfolios can be constructed. The expected returns & variances of returns for each

possible portfolio have to be computed. The identification of efficient portfolios requires the use

of quadratic programming which is a complex procedure.

Because of the difficulties associated with the Markowitz model, it has found little use in

practical applications of portfolio analysis. Simplification is needed in the amount & type of

input data required to perform portfolio analysis. Simplification is also needed in the

computational procedure used to select optimal portfolios.

The simplification is achieved through index models. There are essentially two types of index

models: single index model & multi index model. The single index model is the simplest & the

most widely used simplification & may be regarded as being at one extreme point of a

continuum, with the Markowitz model at the other extreme point. Multi index models may be

placed at the mid region of this continuum of portfolio analysis techniques.



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Single index model/ Market model:

The basic notion underlying the single index model is that all stocks are affected by movements

in the stock market. Casual observation of share prices reveals that when the market moves up

(as measured by any of the widely used stock market indices), prices of most shares tend to

increase. When the market goes down, the prices of most shares tend to decline. This suggests

that one reason why security returns might be co related & there is co-movement between

securities, is because of a common response to market changes. This co-movement of stocks

with a market index may be studied with the help of a simple linear regression analysis, taking

the returns on an individual security as the dependent variable (Ri) & the returns on the market

index (Rm) as the independent variable.

The market model makes three assumptions:

1. The expected value of the error term is zero.

2. The errors are uncorrelated with the market return.

3. The firm specific surprises are uncorrelated across assets.

The return of an individual security is assumed to depend on the return on the market index. The

return of an individual security may be expressed as,

Ri = αi + βi. Rm + ei

Where,

αi = component of security ‘i’s return that is independent of the market’s performance.

Rm = rate of return on the market index.

βi = constant that measures the expected change in R i given a change in Rm.

ei = error term representing the random or residual return.

This equation breaks the return on a stock into two components, one part due to the market & the

other part independent of the market. The beta parameter in the equation, β i, measures how

sensitive a stock’s return is to the return on the market index. It indicates how extensively the

return of a security will vary which changes in the market return. For example if the β i of the

security is 2, then the return of the security is expected to increase by 20% when the market



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return increases by 10%. In this case if the market return decreases by 10%, the security return is

expected to decrease by 20%. A beta co-efficient greater than 1 would suggest greater

responsiveness on the part of the stock in relation to the market & vice-versa.

The alpha parameter αi indicates what the return of the security would be when the market return

is zero. For example, a security with an alpha of +3% would earn 3% return even when the

market return is zero & it would earn an additional 3% at all levels of market return. Conversely,

a security of alpha of -4.5% would lose 4.5% when the market return is zero, & would earn 4.5%

less at all levels of market return. The positive alpha thus represents a sort of bonus return &

would a highly desirable aspect of a security, whereas a negative alpha represents a penalty to

the investor & is an undesirable aspect of a security.

The final term in the equation ei is the unexpected return resulting from influences not identified

by the model. It is referred to as the random or residual return. It may take on any value, but over

a large number of observations it will average out to zero.

William Sharpe who tried to simplify the data inputs & data tabulation required for the

Markowitz model of portfolio analysis, suggested that a satisfactory simplification would be

achieved by abandoning the co variance of each security with each other security & substituting

in its place the relationship of each security with a market index as measured by the single index

model suggested above. This is known as Sharpe index model. In the place of N (N-1)/2 co

variances required for the Markowitz model, Sharpe model would require only N measures of

beta co efficient.



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Measuring security return and risk under single index model:

Using the single index model, expected return on an individual security may be expressed as:

Ri = αi + βi Rm

The return of the security is a combination of two components:

a) A specific return component represented by the alpha of the security ;

b) A market related return component represented by the term βi Rm

The residual return disappears from the expression because its average value is zero, i.e., it has

an expected value of zero.

Correspondingly, the risk of a security σi2 becomes the sum of a market related component and a

component that is specific to the security. Thus,

Total risk = market related risk + specific risk

σi2

= βi2 σm

2 + σei

2

Where,

σi

2= variance of individual security

σm2

= variance of market index returns

σei2

= variance of residual returns of individual security

βi = beta coefficient of individual security

The market related component of risk is referred to as systematic risk as it affects all securities.

The specific risk component is the unique risk or unsystematic risk which can be reduced

through diversification. It is also called diversifiable risk.

The estimates of αI, βi and σei2 of a security are often obtained from regression analysis of

historical data of returns of the security as well as returns of a market index. For any given or

expected value of Rm, the expected return and risk of the security can be calculated.



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For example, if the estimated values of α i, βi and σei2

of a security are 2 percent , 1.5 percent and

300 respectively and if the market index is expected to provide a return of 20 percent with

variance of 120, the expected return and risk of the security can be calculated as below:

Ri = αi + βi Rm

= 2 + 1.5 (20) = 32 percent

σi2= βI

2 σm2 + σei

2

= (1.5)2

(120) + 300

= 570

Measuring portfolio return and risk under single index model:

Portfolio analysis and selection require as inputs the expected portfolio return and risk for all

possible portfolios that can be constructed with a given set of securities. The return and risk of

portfolios can be calculated using the single index model.

Rp = αp + βpRm

The portfolio alpha is the weighted average of the specific returns (alphas) of the individual

securities. Thus,

αp = ωi αi

Where

ωi = proportion of investment in an individual security

αi = specific return of an individual security

The portfolio beta is the weighted average of the Beta coefficients of the individual securities.

Thus,



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βp = ωi βi

Where

ωi = proportion of investment in an individual security

βi = beta coefficient of an individual security

The expected return of the portfolio is the sum of the weighted average of specific returns and

the weighted average of the market related returns of individual securities.

The risk of a portfolio is measured as the variance of the portfolio returns. The risk of a portfolio

is simply a weighted average of market average risks of individual securities plus a weighted

average of the specific risks of individual securities in the portfolio. The portfolio risk may be

expressed as:

σp2

= βp2 σm

2+ ωi

2 σei

2

The first term constitutes the variance of the market index multiplied by the square of portfolio

beta and represents the market related risk (or systematic risk) of the portfolio. The second term

is the weighted average of the variances of residual returns of individual securities and represents

the specific risk or unsystematic risk of the portfolio.

As more and more securities are added to the portfolio, the unsystematic risk of the portfolio

becomes smaller and is negligible for a moderately sized portfolio. Thus, for a large portfolio,

the residual risk or unsystematic risk approaches zero and the portfolio risk becomes equal to

βp2Rm

2. Hence, the effective measure of portfolio risk is βp.



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Let us consider a hypothetical portfolio of four securities. The table below shows the basic input

data such as weightage, alphas, betas and residual variances of the individual securities required

for calculating portfolio variance and return.

Input data

Security Weightage (ωi) Alpha (αi) Beta (βi ) Residual variance

(σei2)

A 0.2 2.0 1.7 370

B 0.1 3.5 0.5 240

C 0.4 1.5 0.7 410

D 0.3 0.75 1.3 285

Portfolio

value

1.0 1.575 1.06 108.45

The values of portfolio alpha, portfolio beta, and portfolio residual variance can be calculated as

first step.

αp = ωi αi

= (0.2) (2) + (0.1) (3.5) + (0.4) (1.5) + ( 0.3) (0.75)

= 1.575

βp = ωi βi

= (0.2) (1.7) + (0.1) (0.5) + (0.4) (0.7) + (0.3) (1.3)

= 1.06

Portfolio residual variance = ωi2 σei

2



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=(0.2)2

(370) + (0.1)2

(240) + (0.4)2

(410) + ( 0.3)2(285)

= 108.45

These values are noted in the last row of the table. Using these values, we can calculate the

expected portfolio return for any value of projected market return. For a market return of 15 per

cent , the expected portfolio return would be:

Rp = αp + βpRm

= 1.575 + (1.06) (15)

= 17.475

For calculating the portfolio variance we need the variance of market returns . Assuming a

market return variance of 320, the portfolio variance can be calculated as:

σp2

= βp2 σm

2+ ωi

2 σei

2

= (1.06)2

(320) + 108.45

= 468.002



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Efficient Frontier with riskless lending and borrowing:

Markowitz’s Efficient Frontier assumes that all securities on the efficient set are risky. But, in

reality, investors usually allocate their wealth across both risky and risk free assets. A risk free

asset is a security that has a return known ahead of time, so the variance of the return is zero.Since risk free asset has a zero correlation with all the points in the feasible region of risky

portfolios, a combination of risk free and any point in the feasible region of risky securities will

be represented by a straight line. With the opportunity of lending and borrowing, the efficient

frontier changes. The straight line dominates the efficient frontier. Since the straight line is

dominating, every investor would do well to choose some combination of risk free and risky

securities. A conservative investor may choose a point nearer to the risk free rate, where an

aggressive investor may choose a point beyond the market portfolio.

Thus the task of portfolio selection can be separated into two steps:

1. Identification of market portfolio, the optimal portfolio for risky securities.

2. Choice of combination of risky and risk free securities, depending on one’s risk attitude.



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Suppose B is the optimal portfolio in the efficient frontier with Rp = 15% and σ = 8%. A risk free

asset with rate of return Rf = 7% is available for investment. If the investor places 40% of his

funds in risk free and remaining 60% in Portfolio B, the return and risk of this combined

portfolio can be calculated using the following formula:

Return:

Rc = WRp + (1-W) Rf

Where,

Rc = expected return on combined portfolio

W = proportion of funds invested in risky portfolio

(1-W) = proportion of funds invested in risk less asset

Rp = Expected return on risky portfolio

Rf = rate of return on risk less asset

Risk:

σc = Wσp + (1-W) σf

σc = standard deviation of the combined portfolio

σp = standard deviation of risky portfolio

σf = standard deviation of risk less portfolio

The second term on the right hand side of the equation (1-W) σf would be zero as σf = zero.

Hence the formula would be reduced to σc = W σp

The return and risk of the combined portfolio is as follows:

Rc = (0.60)(15) + (0.40)(7) = 11.8%



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σc = (0.60)(8) = 4.8%

Both return and risk are lower than those of the risky portfolio B.

If we change the proportion of investment in the risky portfolio to 75%, the return and risk of the

combined portfolio will be:

Rc = (0.75)(15) + (0.25)(7) = 13%

σc = (0.75)(8) = 6%

Here again both return and risk are lower than the risky portfolio B. Similarly, the return and risk

of all possible combinations of the riskless asset and the risky portfolio B may be worked out.

All these points will lie in the straight line.

Now, let us consider borrowing funds by the investor for investing in the risky portfolio an

amount which is larger than his own funds. If W is the proportion of the investor’s funds

invested in the risky portfolio, then we can envisage three situations. If W = 1, the investor’s

funds are fully committed to the risky portfolio. If W < 1, only a fraction of funds is invested in

the risky portfolio and the remainder is lent at risk free rate. If W > 1, it means the investor is

borrowing at the risk free rate and investing an amount larger than his own funds in the risky

portfolio.

The return and risk of such a levered portfolio can be calculated as follows:

RL = WRp – (W-1) Rf

Where,

RL = return on levered portfolio

Rf = the risk free borrowing rate which would be the same as the risk free lending rate, namely

the return on the riskless asset.

Risk of the levered portfolio can be obtained as:

σL = Wσp



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Assume W = 1.25

RL = (1.25)(15) – (0.25)(7) = 17%

σL = (1.25)(8) = 10%

The return and risk of the levered portfolio are larger than those of the risky portfolio. The

levered portfolio would give increased returns with increased risk. The return of all levered

portfolios would lie in a straight line to the right of the market portfolio.



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The Capital Asset Pricing model Consist of 2 elements:

The Capital Market Line

The Security Market Line

Capital Market Line:

The Capital Market Line (CML) is the capital allocation line in a world in which all investors

agree on the expected returns, standard deviations, and correlations of all assets (also known as

the "homogeneous expectations" assumption). Assuming identical expectations, there will be

only one capital allocation line, and it is called the capital market line.

CML is a line representing various efficient portfolios created by combining risk free and risky

securities. All the portfolios lying on this line are efficient in themselves as these provides

maximum returns for a given level of risk or have a minimum risk for a given level of returns. As

per the market efficiency and dominance principle, all the portfolios as well as individual

securities must lie on this line in the long run. This is called CML (Capital Market Line) as it

represents a best set of portfolios on risk and return compendium, which is not only feasible but

also efficient as well. If all investors hold the same risky portfolio, then in equilibrium it must be

the market portfolio. CML generates a line on which the efficient portfolios can lie. Those which

are not efficient will lie below the line. Portfolios having maximum return at each level of risk

are the efficient portfolios. This line is particularly used for portfolios but in rare cases, it is used

for individual securities.

Thus, the CML represents the equilibrium condition that prevails in the market for the portfolios

consisting of risk free and risky investments. All combinations of risky and are bound by CML

and in equilibrium, all investors will end up with portfolio on CML. It says that the expected

The CML defines the relationship between total risk and expected

return for the portfolio consisting of the risk free asset and the

market portfolio.



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return on a portfolio is equal to the risk free rate plus risk premium. The risk premium is equal to

the market price of risk times of quantity of risk. So, the CML shows the tradeoff between the

expected returns and the risk of the portfolios and the risk is measured by the standard deviation

of the portfolio.

Investors at point M, have 100% of their funds invested in the risk free asset . Investors at point

M, have 100% of their funds invested in portfolio M. Between RFR and M, investors hold both

risk free asset and Portfolio M. This means investors are lending some of their funds at risk free

rate and investing the rest in portfolio M. This means they are borrowing funds to buy more of

portrfolio M. The levered positions represnts a 100% investment in portfolio M. and borrowing

to buy even more of portfolio M.

The introduction of risk free asset changes the Markowitz efficient frontier into straight line

called CML.

The equation of CML is

p

M

FMFp σ

σ

R R R R



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The slope of the CML is often called the market price of risk, and equals the reward-to-risk ratio

(or Sharpe ratio} for the market portfolio.The Slope of CML is find out by using the following

formula:

M

FM

σ

R R



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Security Market Line:

The SML provides the relationship between expected returns and of a security or portfolio.

This relationship can be expressed in the form of following equation:

() ( )

Application of SML:

When individual securities and portfolios are priced correctly, they lie exactly on SML.

Securities plotting of the SML , indicate mispricing of securities by market. Securities that plot

above the SML are undervalued and hence attractive because they offer higher expected returns

than required rate of return. The buying pressure of such securities will push up their prices and

lower the return until they are correctly priced. On the other hand, securities that plot below SML

A Graphical representation of CAPM is “Security Market Line”.

This line indicates what rate of return is required to compensate

for the given level of risk.



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are overpriced and hence unattractive as the expected rate of return is lower than required rate of

return.

In a well functioning market, SML can be used to find out the fair rate of return that a security

should offer in view of its beta factor, risk free rate and market rate of return. This fair rate of

return can be compared with actual rate of return on that security. If the fair rate of return is less

than actual rate of return, the security is underpriced. If the fair rate of return is more than actual

rate of return, the security is overpriced.

Example:

Security E(R) %

I 1.4 22

II 1.2 16

III 1.1 14

Other Data Given: = 16%, =6%

Solution:

Whether these securities are correctly priced or not can be found by comparing expected return

of the security with CAPM returns

Security () ( ) Comparing E(R) with

CAPM returns

Underpriced/

Overpriced

I 0.6+1.4(0.16-0.6) = 20% E(R) >CAPM Returns Underpriced

II 0.6+1.2(0.16-0.6) = 20% E(R) < CAPM Returns Overpriced

III 0.6+1.1(0.16-0.6) = 20% E(R) < CAPM Returns Overpriced



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CML vs SML

As discussed earlier, the CML is the efficient frontier, plotting expected returns and standard

deviations (total risk) for portfolios comprising a combination of the risk-free asset and the

market portfolio. If markets are in equilibrium, risk and return combinations for individual

securities will lie along the SML, but not along the CML. Risk and return combinations for

individual securities will lie below the CML because their standard deviations include

unsystematic risk that is diversified away in the market portfolio.

SML CML

Measure of risk Uses systematic risk Uses Standard Deviation

Application Tool used to determine theappropriate expected returns

for securites

Tool used to determine theappropriate asset allocation for

the investor

Definition \Graph of the Capital Asset

Pricing Model

Graph of the Efficient frontier

Slope Market risk premium Market portfolio Sharpe ratio

The CML uses total risk = σp on the x-axis. Hence, only efficient portfolis will plot on the CML.

On the other hand, the SML uses beta (systematic risk) on the x-axis. So in a CAPM world, all

properly priced securities and portfolios of securities will plot on the SML

Example: Using the SML

A stock has a beta of 0.75 and an expected return of 13%. The risk-free rate is 4%.

Calculate the market risk premium and the expected return on the market portfolio.

Answer:

According to the SML: 0.13 = 0.04 + 0.75[E(RM)- Rp].

Therefore, the market risk premium is equal to: [E(Rm)- Rf ] = 0.12 = 12%.

The expected return on the market is calculated as: [E(Rm) - 0.04] = 0.12,

or E(RM) = 0.16 = 16%.



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Capital asset pricing model:

In finance, the capital asset pricing model (CAPM) is used to determine a theoretically

appropriate required rate of return of an asset, if that asset is to be added to an already well-

diversified portfolio, given that asset's non-diversifiable risk. The model takes into account the

asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often

represented by the quantity beta (β) in the financial industry, as well as the expected return of the

market and the expected return of a theoretical risk-free asset.

The model was introduced by Jack Treynor (1961, 1962), William Sharpe (1964), John

Lintner (1965a,b) and Jan Mossin (1966) independently, building on the earlier work of Harry

Markowitz on diversification and modern portfolio theory. Sharpe, Markowitz and Merton

Miller jointly received the Nobel Memorial Prize in Economics for this contribution to the field

of financial economics.

CAPM assumptions:

1. Investors make their decisions on the basis of risk-return assessments measured in terms

of expected returns and standard deviation of returns.

2. The purchase or sale of a security can be undertaken in infinitely divisible units.

3. Purchases and sales by a single investor cannot affect prices. This means there is perfect

competition where investors in total determine prices by their actions.

4. There are no transaction costs. Given the fact that transaction costs are small, they are

probably of minor importance in investment decision-making, and hence they are

ignored.

5. There are no personal income taxes. Alternatively, the tax rates on dividend income and

capital gains are the same, thereby making the investor indifferent to the form in which

the return on the investment is received (dividends or capital gains).

6. The investor can lend or borrow any amount of funds desired at a rate of interest equal to

the rate for riskless securities.

7. The investor can sell short any amount of any shares.



27 | P a g e

8. Investors share homogeneity of expectations. This implies that investors have identical

expectations with regard to the decision period and decision inputs. Investors are

presumed to have identical holding periods and also identical expectations regarding

expected returns, variances of expected returns and co variances of all pairs of securities.

The CAPM is a model for pricing an individual security or portfolio. For individual securities,

we make use of the security market line (SML) and its relation to expected return and systematic

risk (beta) to show how the market must price individual securities in relation to their security

risk class. The SML enables us to calculate the reward-to-risk ratio for any security in relation to

that of the overall market. Therefore, when the expected rate of return for any security is deflated

by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal

to the market reward-to-risk ratio, thus:

Market reward-to-risk ratio is effectively the market risk premium and by rearranging the above

equation and solving for E(Ri), we obtain the Capital Asset Pricing Model (CAPM).

where:

is the expected return on the capital asset

is the risk-free rate of interest such as interest arising from government bonds

(the beta) is the sensitivity of the expected excess asset returns to the expected

excess market returns, or also ,

is the expected return of the market

http://en.wikipedia.org/wiki/Security_market_line

http://en.wikipedia.org/wiki/Systematic_risk




http://en.wikipedia.org/wiki/Risk_premium

http://en.wikipedia.org/wiki/Beta_(finance)



http://en.wikipedia.org/wiki/Sensitivity_and_specificity

http://en.wikipedia.org/wiki/Sensitivity_and_specificity


http://en.wikipedia.org/wiki/Risk_premium



http://en.wikipedia.org/wiki/Security_market_line



is sometimes known as the market premium (the difference

between the expected market rate of return and the risk-free rate of return).

is also known as the risk premium

Restated, in terms of risk premium, we find that:

Which states that the individual risk premium equals the market premium times β

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capm vs market model

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